A new statistical method is described for detecting state changes in the electroencephalogram (EEG), based on the ongoing relationships between electrode voltages at different scalp locations. An EEG sleep recording from one NREM-REM sleep cycle from a healthy subject was used for exploratory analysis. A dimensionless function defined at discrete times ti, u(ti), was calculated by determining the log-likelihood of observing all scalp electrode voltages under the assumption that the data can be modeled by linear combinations of stationary relationships between derivations. The u(ti), calculated by using independent component analysis, provided a sensitive, but non-specific measure of changes in the global pattern of the EEG. In stage 2, abrupt increases in u(ti) corresponded to sleep spindles. In stages 3 and 4, low frequency (≈ 0.6 Hz) oscillations occurred in u(ti) which may correspond to slow oscillations described in cellular recordings and the EEG of sleeping cats. In stage 4 sleep, additional irregular very low frequency (≈ 0.05–0.2 Hz) oscillations were observed in u(ti) consistent with possible cyclic changes in cerebral blood flow or changes of vigilance and muscle tone. These preliminary results suggest that the new method can detect subtle changes in the overall pattern of the EEG without the necessity of making tenuous assumptions about stationarity.